Custom Chain Breaks When Animated no matter what
I looked at your file and made out some problems. 


Scale was not applied. For any kind of simulation, you would want your scale values to be 1, 1, 1, so after you scaled an object in object mode, hit CtrlA and choose 'scale' to apply it.
The objects were very large. In the scene tab choose a unit system (metric or imperial) to get an idea of the overall scale of your objects. Once I got them ready for simulation (step 3), they were falling very slow, because they had to travel several meters.
Keep your topology clean. Something went quite wrong with your objects, the topology is completely messed up. It also is very dense, that caused your long simulation times. (The numbers of verts are for the whole scene)





The collision margin was way too high. That caused the links to "jump off" as soon, as the simulation started.


What I couldn't fix is the jittering. To make it work somehow, I dialed down the gravity influence of the rigid body world, but that cannot be the solution. Could anyone take a second look at the files and explain, why the jittering is happening?
Also: the solver somehow has problems with the uppermost hook. I removed the rigid body collision from that one and placed some cylinders. Whenever you can, I would recommend to use the collision primitives in the rigid body settings. That is unfortunately not possible for your animation, because the objects intersect with eachother.

Here is the (partially) fixed .blend:


I hope this brings you a bit closer to your goal.